To make maple and agave syrup shortcrust pastry, place butter and flour in a food processor and process until mixture resembles coarse breadcrumbs. Add syrup and process until mixture just forms a ball. (You may need to add up to 2 tsp extra syrup, until dough comes together.) Shape dough into a disc. Wrap in plastic wrap and chill for 1 hr.
Place pastry between two sheets of baking paper and roll out until 3mm thick. Use to line base and sides of a 2cm-deep, 22cm loose-based tart pan with. Use a small, sharp knife to trim edges. Chill for 30 mins.
Preheat oven to 180C/160C fan. Line pastry case with baking paper and fill with baking weights, rice or dried beans. Blind bake for 15 mins. Remove baking paper and weights, and bake for 7-10 mins, until pastry browns lightly. Cool completely.
To make frangipane filling, using an electric mixture and a large bowl, beat butter and maple and agave syrup until combined. Add egg yolk and beat to combine. Add almond meal and flour, and beat to combine. Spoon mixture into pastry case. Smooth surface. Top with apple slices and spray with oil.
Bake tart for 30 mins, until frangipane is set and lightly browned. While still warm, brush with extra maple and agave syrup. Cool slightly. Serve tart warm or at room temperature.
To prevent the apple slices from browning, brush them with a little lemon juice.